On the relation of negations in Nelson algebras-Reference-Cited by-同舟云学术

On the relation of negations in Nelson algebras

Published:2021 Issue: Volume:56 Page:15-56
ISSN:2084-2589
Container-title:Reports on Mathematical Logic
language:en
Short-container-title:

Author:

Gomez Conrado¹,Marcos Miguel Andres²,San Martin Hernan Javier³

Affiliation:

1. Instituto de Matematica Aplicada del Litoral, UNL, CONICET, FIQ. Predio Dr. Alberto Cassano del CCT-CONICET-Santa Fe, Colectora de la Ruta Nacional no. 168, Santa Fe (3000), Argentina

2. Facultad de Ingenieria Quimica, CONICET-Universidad Nacional del Litoral. Santiago del Estero 2829, Santa Fe (3000), Argentina

3. Departamento de Matematica, Facultad de Ciencias Exactas (UNLP), and CONICET. Casilla de correos 172, La Plata (1900), Argentina

Abstract

The aim of this paper is to investigate the relation between the strong and the "weak" or intuitionistic negation in Nelson algebras. To do this, we define the variety of Kleene algebras with intuitionistic negation and explore the Kalman's construction for pseudocomplemented distributive lattices. We also study the centered algebras of this variety.

Publisher

Uniwersytet Jagiellonski - Wydawnictwo Uniwersytetu Jagiellonskiego

Subject

Logic,Philosophy

Reference30 articles.

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3. D. Brignole, Equational Characterization of Nelson Algebras, Notre Dame J. Formal Logic 10 (1969), 285{297. Reproduced in Notas de Logica Matematica no. 9 (1974), Universidad Nacional del Sur, Baha Blanca.

4. M. Busaniche and R. Cignoli, Constructive Logic with Strong Negation as a Substructural Logic, Journal of Logic and Computation 20:4 (2010), 761-793.

5. J.L. Castiglioni, S. Celani, and H.J. San Martin, Kleene algebras with implication, Algebra Universalis 77:4 (2017) 375-393.